In a broadcast apparently marking the girls' third month in captivity, Abubakar Shekau, the Boko Haram leader, said they would not be freed until the government released the "army" of the group's fighters held in Nigerian jails.

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Mr Shekau also claimed responsibility for three bombings last month and voiced support for Islamic State, the extremists who have seized much of northern Iraq.

The video served as a direct snub to Malala Yousafzai, the Pakistani schoolgirl and women's rights campaigner who arrived in Nigerian capital, Abuja, over the weekend to voice support for the #bringbackourgirls campaign.

Pakistani activist Malala Yousafzai. who survived being shot by the Taliban. holds a picture of kidnapped schoolgirl Sarah Samuel with her mother Rebecca Samuel, in Abuja, Nigeria. Photo: AP/Olamikan Gbemiga)

Ms Yousafzai, 17, who moved to Britain after being shot by the Taliban, met parents of the missing girls yesterday and was also expected to hold talks with Goodluck Jonathan, Nigeria's president.

As she did so, serious doubts emerged about the girls' chances of ever being rescued. In briefings with The Daily Telegraph over the weekend, Western diplomats said that, despite international publicity, the efforts to find the hostages were little further on than they were in May, when Britain, America and France began to help. With neither a prisoner swap or a rescue considered likely, there was little real prospect of any "breakthrough" in the foreseeable future, they said.

One diplomat said: "It is hard to see this being resolved either by a rescue or a prisoner swap deal, although that is also true for a lot of other girls kidnapped by Boko Haram in recent months and years, who are now bush wives. What may happen is that from time to time, some may seize a chance to escape, or a deal may be done with one particular local faction that is holding some of the hostages. Over the course of a few months or years they may begin to reappear."

The diplomats' gloomy assessment is likely to dismay the girls' families, whose hopes of being reunited with them have been sustained largely by the scale of the international response. On Sunday, Malala, described the girls as "sisters" and said she was going to "speak up for them until they are released".

Diplomats say the reality is that even if the girls could be located - which is hard, given that the area being searched is "twice the size of Belgium" - it would be impossible to mount a rescue without Boko Haram killing a large number first.

Western governments have also explicitly told Mr Jonathan not to agree to Boko Haram's demands for a prisoner swap, saying there should be no negotiations with such a ruthless terrorist group. In the 16-minute video, Mr Shekau addressed that point explicitly. "Bring Back Our Girls... bring back our army," he said, referring to the Boko Haram fighters currently in custody.

While reports have emerged in recent weeks of indirect contacts between Boko Haram and the government with a view to a prisoner swap, diplomats say most of the negotiations have been isolated, independent initiatives without any centralised command, or any connection to Mr Jonathan's office. Many in the Nigerian government and military also strongly oppose any kind of swap, and would try to derail any such plan even if it had Mr Jonathan's backing, said one Western official.

In the video, Boko Haram also claimed responsibility for a bomb in a shopping centre in Abuja on June 25 that killed 22 people, and for two explosions the same day at a fuel depot in Lagos, Nigeria's commercial hub.

Nigerian officials had previously claimed the two Lagos blasts were caused by a gas leak in order to avoid causing panic in the city, which has so far largely escaped Boko Haram's violence. But security sources have privately admitted that at least one of the blasts was caused by a female suicide bomber, and Mr Shekau boasted of personally ordering the volunteer "who went and detonated it".

Mr Shekau, who appeared in the video flanked by at least 10 gunmen in front of two armoured personnel carriers, also expressed support for the Abubakar Al-Baghdadi, the leader of the Islamic State, Ayman al-Zawahiri, the leader of al-Qaeda, and Mullah Omar, the leader of the Taliban.